That's it. Rock the workout on Tuesday and knock out the long run on Saturday. This schedule works well for numerous reasons. First, you can have a solid day at work on Monday without the burden of a hard training session.
Monday is a maintenance day. You simply maintain your aerobic fitness and your leg speed by doing four to five strides at 5K pace with 60 seconds of easy jogging between the strides. Complete these strides as part of your run, so this seven-to-eight-minute segment should be done in the middle of your run. Strides done on maintenance days keep your leg speed up but, neuromuscularly, they also prepare your legs for the workout on Tuesday.
More: Run Fast With Strides
On Tuesday, you should be able to carve out the time not only to get the workout in but also to complete general strength and mobility exercises, and active isolated flexibility after the workout.
Wednesday is the "it depends" day. If you can handle five days a week of running, then you should run. If you've been running five days a week for some time, then you can run a bit longer than your normal maintenance-day run. But if you're a new runner or new to the half-marathon distance, you should definitely cross-train on this day. And please go easy if you're cross-training—you need to recover from Tuesday, and if you're less experienced, you aren't ready for two hard days back to back.
Thursday is a cross-training day if you run five days a week. But Thursday is also a good day to take off, and if you're only running four days a week, I highly recommend that you take this day off. Furthermore, if you run five days a week most weeks, and feel fatigue, take Thursday off. Don't feel guilty about it. You need to get back to feeling energetic if you want to do quality training.
Friday is the same as Monday. The strides on Friday make the pace of the long run on Saturday feel good.
The Saturday long run is the most important day of the week. You need to get up early, have your normal race-day breakfast, or experiment with food to dial in what your race-day breakfast should be, and be ready to have a solid run.
Sometimes this run is just about getting in the time on your feet. For instance, if you run 4 to 5 miles three days a week, and have identified a half marathon you want to run in eight weeks, then this run will never be fast. Rather, you'll build up your mileage over the course of the eight weeks.
If you've run many half marathons and your goal is to PR, then you should consider running some of these long runs as progression runs, which are runs that start easy then gradually increase in pace and end at a hard, but controlled pace. Regardless of where you are in your evolution as a half-marathon runner, the long run is the most important workout of the week.